# If a is m x r and b is n x r then 
#
#   apply(outer(a,t(b),"-"),c(1,4),function(x)sqrt(sum(diag(x*x))))
#
# is the m x n matrix of distances between the m rows of a and 
# n rows of b.
#
# Modify, as necessary, if you want distances other than euclidean.
#
# The following code is 10-100 times faster.

distmat <- function(X, Y)
#   Computes Euclidean distance between two vectors as:
#       ||A-B|| = sqrt ( ||A||^2 + ||B||^2 - 2*A.B )
#   and vectorizes to rows in two matrices (or vectors).
{
    if (!is.numeric(X) || !is.numeric(Y))
        stop("X and Y must be numeric vectors or matrices.")
    if (is.vector(X)) dim(X) <- c(1,length(X))
    if (is.vector(Y)) dim(Y) <- c(1,length(Y))
    if (ncol(X) != ncol(Y))
        stop("X and Y must have the same number of columns.")

    m  <- nrow(X); n <- nrow(Y)
    XY <- X %*% t(Y)    # (m,n)-matrix
    XX <- matrix( rep(apply(X*X, 1, sum), n), m, n, byrow=F )
    YY <- matrix( rep(apply(Y*Y, 1, sum), m), m, n, byrow=T )

    sqrt(XX + YY - 2*XY)
}
